Joint economic model for totally adaptive X and R charts

Recent studies have shown that the amount of cost savings produced by a Vp X chart designed economically is higher than the fixed parameter X chart. This paper extends these studies for processes that are monitored jointly by X and R charts having all design parameters varying adaptively. We develop a joint expected cost model for a process whose mean is controlled by a Vp X chart and whose variance is controlled by a Vp R chart. The cost function due to controlling the process quality through these Vp charts is derived. This model provides a tool for optimal selection of the design parameters, in this way the minimum cost can be obtained. The possible savings provided by the developed model can be assessed.